The floor could be creaking due to improper installation (not enough nails, not enough adhesive, no room for expansion), or water leaking on the flooring which makes the joints expand, or not enough ventilation in bathroom, i.e. if there is no ceiling vent or the vent is not large enough.
If you have a cracked tub, you should check it immediately and have it repaired by a professional. Leaking water can cause serious damage to your home. If it is just a crack you want to fix, find a handy man to help you. If you want to remodel the entire room, you will need a licensed general contractor.
The tub is creaking because it probably isn’t set in a bed or mortar. Is it an acrylic tub or a thin gauge metal tub? Cast iron tubs wont creak generally because they weigh in at 250-350 lbs.
We do dozens of bathrooms yearly and i always urge my customer to aim for a good quality tub, whether it be cast iron or a heavy duty Kohler or Americast style that is heavy enough to not need to set in a bed of mortar
If the creak sounds like a nail pulling from wood, no. If the tub visibly moves, yes.
Most likely due to improper installation.
The bottom of a bathtub is higher than its surrounds due to plumbing connection needs.
When a bathtub is installed, the portion below the bottom, should sit on mudset, without compromising the accessibility to the drain connection. This will ensure that once the bathtub is filled with water, and or a person is standing inside, its bottom does not flexes downward, which would cause movement of its surrounds causing minor movements with consequent noises.